Abstract:

This is a nontechnical introduction to recent work on
quantum gravity using ideas from higher-dimensional algebra.
We argue that reconciling general relativity with the
Standard Model requires a `background-free quantum theory with
local degrees of freedom propagating causally'. We describe
the insights provided by work on topological quantum field theories
such as quantum gravity in 3-dimensional spacetime. These are
background-free quantum theories lacking local degrees of freedom,
so they only display some of the features we seek. However, they
suggest a deep link between the concepts of `space' and `state',
and similarly those of `spacetime' and `process', which we argue
is to be expected in any background-free quantum theory. We sketch
how higher-dimensional algebra provides the mathematical tools to
make this link precise. Finally, we comment on attempts to formulate
a theory of quantum gravity in 4-dimensional spacetime using
`spin networks' and `spin foams'.